"Has smaller fleas that on him prey; And these have smaller still to bite 'em, And so proceed ""ad infinitum"". Thus every poet, in his kind, Is bit by him that comes behind</poem> __notoc__ Ad infinitum Ad infinitum is a Latin phrase meaning ""to infinity"" or ""forevermore"". In context, it usually means ""continue forever, without limit"" and this can be used to describe a non-terminating process, a non-terminating ""repeating"" process, or a set of instructions to be repeated ""forever,"" among other uses. It may also be used in a manner similar to the Latin phrase ""et cetera"" to denote written"
"Infinitive Infinitive (abbreviated ) is a grammatical term referring to certain verb forms existing in many languages, most often used as non-finite verbs. As with many linguistic concepts, there is not a single definition applicable to all languages. The word is derived from Late Latin ""[modus] infinitivus"", a derivative of ""infinitus"" meaning ""unlimited"". In traditional descriptions of English, the infinitive is the basic dictionary form of a verb when used non-finitely, with or without the particle ""to"". Thus ""to go"" is an infinitive, as is ""go"" in a sentence like ""I must go there"" (but not in ""I go there"","
"Infinity Infinity (symbol: ) is a concept describing something without any bound or larger than any natural number. Philosophers have speculated about the nature of the infinite, for example Zeno of Elea, who proposed many paradoxes involving infinity, and Eudoxus of Cnidus, who used the idea of infinitely small quantities in his method of exhaustion. Modern mathematics uses the general concept of infinity in the solution of many practical and theoretical problems, such as in calculus and set theory, and the idea is also used in physics and the other sciences. In mathematics, ""infinity"" is often treated as a number"
"Absolute Infinite The Absolute Infinite (""symbol"": Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. It can be thought as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite. Cantor linked the Absolute Infinite with God, and believed that it had various mathematical properties, including the reflection principle: every property of the Absolute Infinite is also held by some smaller object. Cantor said: Cantor also mentioned the idea in his letters to Richard Dedekind (text in square brackets not present in original): The idea that the collection of all"
"the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction. (C.F. Gauss [in a letter to Schumacher, 12 July 1831]) The drastic change was initialized by Bolzano and Cantor in the 19th century. Bernard Bolzano who introduced the notion of ""set"" (in German: ""Menge"") and Georg Cantor who introduced set theory opposed the general attitude. Cantor distinguished three realms of infinity: (1) the infinity of God (which he called"
"Eternity Eternity in common parlance is an infinitely long period of time. In classical philosophy, however, eternity is defined as what exists outside time while sempiternity is the concept that corresponds to the colloquial definition of eternity. Eternity is an important concept in many religions, where the god or gods are said to endure eternally. Some, such as Aristotle, would say the same about the natural cosmos in regard to both past and future eternal duration, and like the eternal Platonic forms, immutability was considered essential. Aristotle argued that the cosmos has no beginning. In Aristotle's Metaphysics, eternity is the"
"in Latin as ' ""for eternity and beyond"", and in English Bible translations usually as ""for ever and ever"". In Aramaic, however, the same phrase was rendered as (""lalmey almaya"", literally ""from the eternity of eternities"" or ""from the world of worlds""), for instance in the Kaddish, an important prayer in the Jewish liturgy. In saecula saeculorum The Latin phrase expresses the idea of eternity and is literally translated as ""unto the ages of ages."" The phrase occurs in the New Testament in the Vulgate and translates the original Koine Greek phrase """" (""eis toùs aionas ton aiṓnōn""), found e.g."
"still fills all Creation, without any change at all from God's perspective. In Habad systemisation of Hasidic thought, the term ""Ein Sof"" (""Unlimited"" Infinite) itself does not capture the very essence of God. Instead it uses the term ""Atzmus"" (the Divine ""Essence""). The Ein Sof, while beyond all differentiation or limitation, is restricted to Infinite expression. The true Divine essence is above even Infinite-Finite relationship. God's essence can be equally manifest in finitude as in infinitude, as found in the Talmudic statement that the Ark of the Covenant in the First Temple took up no space. While it measured its"
"Infinitism Infinitism is the view that knowledge may be justified by an infinite chain of reasons. It belongs to epistemology, the branch of philosophy that considers the possibility, nature, and means of knowledge. Since Gettier, ""knowledge"" is no longer widely accepted as meaning ""justified true belief"" only. However, some epistemologists still consider knowledge to have a justification condition. Traditional theories of justification (foundationalism and coherentism) and indeed some philosophers consider an infinite regress not to be a valid justification. In their view, if ""A"" is justified by ""B"", ""B"" by ""C"", and so forth, then either Infinitism, the view, for"
"order to/so that"" with the past tense form (most probably remnant of subjunctive) of the verb: ""Я хочу, чтобы вы ушли"" (literally, ""I want so that you left""). Infinitive Infinitive (abbreviated ) is a grammatical term referring to certain verb forms existing in many languages, most often used as non-finite verbs. As with many linguistic concepts, there is not a single definition applicable to all languages. The word is derived from Late Latin ""[modus] infinitivus"", a derivative of ""infinitus"" meaning ""unlimited"". In traditional descriptions of English, the infinitive is the basic dictionary form of a verb when used non-finitely, with"
"foundations of mathematics such as New Foundations by Willard Van Orman Quine. Absolute Infinite The Absolute Infinite (""symbol"": Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. It can be thought as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite. Cantor linked the Absolute Infinite with God, and believed that it had various mathematical properties, including the reflection principle: every property of the Absolute Infinite is also held by some smaller object. Cantor said: Cantor also mentioned the idea in his letters to Richard Dedekind (text in square"
"Aevum In Scholastic philosophy, the aevum (also called aeviternity) is the mode of existence experienced by angels and by the saints in heaven. In some ways, it is a state that logically lies between the eternity (timelessness) of God and the temporal experience of material beings. It is sometimes referred to as ""improper eternity"". The word ""aevum"" is Latin, originally signifying ""age"", ""aeon"", or ""everlasting time""; the word ""aeviternity"" comes from the Medieval Latin neologism ""aeviternitas"". The concept of the aevum dates back at least to Albertus Magnus's treatise ""De quattuor coaequaevis"". Its most familiar description is found in the"
"Infinity (philosophy) In philosophy and theology, infinity is explored in articles under headings such as the Ultimate, the Absolute, God, and Zeno's paradoxes. In Greek philosophy, for example in Anaximander, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (ἄπειρον, ""apeiron""). The Jain metaphysics and mathematics was the first to define and delineate different ""types"" of infinities. The work of the mathematician Georg Cantor first placed infinity into a coherent mathematical framework. Keenly aware of his departure from traditional wisdom, Cantor also presented a comprehensive historical"
"for eternity. This state shares some similarities with certain Christian views of hell. On this subject, Joseph Smith taught that those who commit the unpardonable sin are ""doomed to ""Gnolaum""—to dwell in hell, worlds without end."" The word ""gnolaum"" is used elsewhere by Smith to mean ""eternal"" (in the sense of 'everlasting' or 'forever' with perpetuity in time, and likely not ""eternal"" as 'outside of time' or having no relationship with the temporality). It is believed by Latter-day Saints that ""few"" people who have lived on the earth will be consigned to this state, but Latter-day Saint scripture suggests that"
"Apeiron Apeiron (; ) is a Greek word meaning ""(that which is) unlimited,"" ""boundless"", ""infinite"", or ""indefinite"" from ""a-"", ""without"" and ""peirar"", ""end, limit"", ""boundary"", the Ionic Greek form of ""peras"", ""end, limit, boundary"". It is akin to Persian ""piramon"", meaning ""boundary, circumference, surrounding"". The ""apeiron"" is central to the cosmological theory created by Anaximander, a 6th-century BC pre-Socratic Greek philosopher whose work is mostly lost. From the few existing fragments, we learn that he believed the beginning or ultimate reality (""arche"") is eternal and infinite, or boundless (""apeiron""), subject to neither old age nor decay, which perpetually yields fresh"
"Actual infinity In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given, actual, completed objects. This is contrasted with potential infinity, in which a non-terminating process (such as ""add 1 to the previous number"") produces a sequence with no last element, and each individual result is finite and is achieved in a finite number of steps. The ancient Greek term for the potential or improper infinite was ""apeiron"" (unlimited or"
"is mentioned by Plato: Nothing can exist if it doesn't contain continually and simultaneously the limited and the unlimited, the definite and the indefinite. Some doctrines existing in Western thought, still transmit some of the original ideas: ""God ordained that all men shall die"", ""Death is a common debt"". The Greek word ""adikia"" (injustice) transmits the notion that someone has operated outside of his own sphere, without respecting the one of his neighbour. Therefore, he commits hubris. The relative English word ""arrogance"" (claim as one's own without justification; ), is very close to the original meaning of the aphorism: ""Nothing"
"Infinite product In mathematics, for a sequence of complex numbers ""a"", ""a"", ""a"", ... the infinite product is defined to be the limit of the partial products ""a""""a""...""a"" as ""n"" increases without bound. The product is said to ""converge"" when the limit exists and is not zero. Otherwise the product is said to ""diverge"". A limit of zero is treated specially in order to obtain results analogous to those for infinite sums. Some sources allow convergence to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity"
"during 1957. Infinity (philosophy) In philosophy and theology, infinity is explored in articles under headings such as the Ultimate, the Absolute, God, and Zeno's paradoxes. In Greek philosophy, for example in Anaximander, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (ἄπειρον, ""apeiron""). The Jain metaphysics and mathematics was the first to define and delineate different ""types"" of infinities. The work of the mathematician Georg Cantor first placed infinity into a coherent mathematical framework. Keenly aware of his departure from traditional wisdom, Cantor also presented a"
"states that the Buddha taught the Infinite Meanings just before expounding the ""Lotus Sutra"". For Buddhists, the term ""Innumerable Meanings"" or ""Infinite Meanings"" is used in two senses. The first, used in the singular, refers to the true aspect of all things, the true nature of all forms in the universe. The second sense, used in the plural, refers to the countless appearances or phenomena of the physical, visible world. All of these countless appearances are brought forth by the one true, pure world – the true aspect of all things (the one true Dharma of ""nonform""). This is the"
"indefinite), in contrast to the actual or proper infinite ""aphorismenon"". ""Apeiron"" stands opposed to that which has a ""peras"" (limit). These notions are today denoted by ""potentially infinite"" and ""actually infinite"", respectively. Anaximander (610–546 BC) held that the "" apeiron"" was the principle or main element composing all things. Clearly, the 'apeiron' was some sort of basic substance. Plato's notion of the ""apeiron"" is more abstract, having to do with indefinite variability. The main dialogues where Plato discusses the 'apeiron' are the late dialogues ""Parmenides"" and the ""Philebus"". Aristotle sums up the views of his predecessors on infinity thus: ""Only"
"this and other ways. Variations of chess played on an unbounded board are called infinite chess. Cognitive scientist George Lakoff considers the concept of infinity in mathematics and the sciences as a metaphor. This perspective is based on the basic metaphor of infinity (BMI), defined as the ever-increasing sequence <1,2,3...>. The symbol is often used romantically to represent eternal love. Several types of jewelry are fashioned into the infinity shape for this purpose. Infinity Infinity (symbol: ) is a concept describing something without any bound or larger than any natural number. Philosophers have speculated about the nature of the infinite,"
"unmoved mover (God), understood as the gradient of total synergy (""produces motion by being loved""). Boethius defined eternity as ""simultaneously full and perfect possession of interminable life"". Eternity is often symbolized by the image of a snake swallowing its own tail, known as the Ouroboros (or Uroboros). The circle is also commonly used as a symbol for eternity, as is the mathematical symbol of infinity, formula_1. Symbolically, it suggests that Eternity has no beginning or end. Eternity Eternity in common parlance is an infinitely long period of time. In classical philosophy, however, eternity is defined as what exists outside time"
"Ad vitam aut culpam Ad vitam aut culpam is a Latin phrase found in Scots law which meaning ""for life or until fault"" which guarantees the right of a Sheriff Depute (judge) to hold office permanently or until they forfeit such by misconduct. The Heritable Jurisdictions (Scotland) Act 1746 used the phrase to guarantee a Sheriff's term office after they have held office for seven years. The applicability of this law was decided upon by the House of Lords in the case ""Stewart v. Secretary of State For Scotland"" where it was stated this it did not protect a Sheriff"
"Ananta (infinite) Ananta is a Sanskrit term which means 'endless' or 'limitless', also means 'eternal' or 'infinity', in other words, it also means infinitude or an unending expansion or without limit. It is one of the many names of Lord Vishnu. Ananta is the Shesha-naga, the celestial snake, on which Lord Vishnu reclines. In the Mahabharata, Ananta or Adi-sesa, the serpent, or Vasuki, is the son of Kasyapa, one of the Prajapatis, through Kadru as her eldest son. Kadru had asked her sons to stay suspended in the hair of Airavata’s tail who on refusing to do so were cursed"
"Infinitesimal In mathematics, infinitesimals are things so small that there is no way to measure them. The insight with exploiting infinitesimals was that entities could still retain certain specific properties, such as angle or slope, even though these entities were quantitatively small. The word ""infinitesimal"" comes from a 17th-century Modern Latin coinage ""infinitesimus"", which originally referred to the ""infinite-th"" item in a sequence. Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is"
"elsewhere states that ""the chief punishment of hell is that of eternal separation from God"" (para 1035). The question is what ""eternal"" means in this context. Thomas Aquinas, following Boethius, states that ""eternity is the full, perfect and simultaneous possession of unending life"" (""Summa Theologica"" I, question 10), so apparently eternal separation from God is a ""negative eternity"", a complete and permanent separation from God. In the Collect (opening prayer) for the eighth Sunday after Pentecost in the Tridentine missal, we find the words """"qui sine te esse non possumus"""", meaning ""we who without Thee cannot be (or exist)"". Putting"
"Atzmus Atzmus/Atzmut ( from the Hebrew ""Etzem"" ) meaning ""essence"", is the descriptive term referred to in Kabbalah, and explored in Hasidic thought, for the Divine essence. Classical Kabbalah predominantly refers to the Godhead in Judaism with its designated term ""Ein Sof"" (""No end""-Infinite), as this distinguishes between the Divine Being beyond description and manifestation, and Divine emanations within Creation, which become the descriptive concern of systemised Kabbalistic categorisation. Reference to ""Atzmus"" is usually restricted in Kabbalistic theory to discussion whether ""Ein Sof"" represents the ultimate Divine Being in Itself, or to God as first cause of Creation. Hasidic thought"
"total of creation"". The explanation Summum offers is based upon what it calls the ""Grand Principle of Creation,"" and via this grand principle, The All (SUMMUM) exists. In summary, according to the Summum philosophy, The All is a union between Nothing and All Possibility, the ultimate opposites, and the nature of that union is without beginning or end for these two opposites automatically and simultaneously create each other. The result is a ""cosmic copulation"" whose effect is an infinite, living mind. The All The All (also called The One, The Absolute, The Great One, The Creator, The Supreme Mind, The"
"In saecula saeculorum The Latin phrase expresses the idea of eternity and is literally translated as ""unto the ages of ages."" The phrase occurs in the New Testament in the Vulgate and translates the original Koine Greek phrase """" (""eis toùs aionas ton aiṓnōn""), found e.g. at Phillippians 4:20. The phrase expresses the eternal duration of God's attributes. Other variations of the phrase are found at e.g. Eph 3:21, as εἰς πάσας τὰς γενεὰς τοῦ αἰῶνος τῶν αἰώνων, ἀμήν, here referring to the glory of God the Father; this may be translated as ""from all generations for ever and ever,"
"But A is here said to be in a certain relation to the relation R¹. So that we can express the same fact by saying, ""A is in the relation R¹ to the relation R¹ to the relation R to B"", and so on ""ad infinitum"". A predicate which can thus be analyzed into parts all homogeneous with the whole I call a ""continuous predicate"". It is very important in logical analysis, because a continuous predicate obviously cannot be a ""compound"" except of continuous predicates, and thus when we have carried analysis so far as to leave only a continuous"
"eternal. The first premise is defended by a reductio ad absurdum where Philoponus shows that actual infinites can not exist in the actual world because they would lead to contradictions albeit being a possible mathematical enterprise. Since an actual infinite in reality would create logical contradictions, it can not exist including the actual infinite set of past events. The second argument, the ""argument from the impossibility of completing an actual infinite by successive addition"", states: The first statement states, correctly, that a finite (number) cannot be made into an infinite one by the finite addition of more finite numbers. The"
"Brahman Brahman (ब्रह्म) connotes the highest Universal Principle, the Ultimate Reality in the universe. In major schools of Hindu philosophy, it is the material, efficient, formal and final cause of all that exists. It is the pervasive, genderless, infinite, eternal truth and bliss which does not change, yet is the cause of all changes. Brahman as a metaphysical concept is the single binding unity behind diversity in all that exists in the universe. In the Upanishads, it has been variously described as ""Sat-cit-ānanda"" (truth-consciousness-bliss) and as the unchanging, permanent, highest reality. Brahman is discussed in Hindu texts with the concept"